R/L2HardThr.R

In JSparO: Joint Sparse Optimization via Proximal Gradient Method for Cell Fate Conversion

#' @title L2HardThr - Iterative Hard Thresholding Algorithm based on \eqn{l_{2,0}} norm
#' @description The function aims to solve \eqn{l_{2,0}} regularized least squares.
#' @param A Gene expression data of transcriptome factors (i.e. feature matrix in machine learning).
#' The dimension of A is m * n.
#' @param B Gene expression data of target genes (i.e. observation matrix in machine learning).
#' The dimension of B is m * t.
#' @param X Gene expression data of Chromatin immunoprecipitation or other matrix
#' (i.e. initial iterative point in machine learning). The dimension of X is n * t.
#' @param s joint sparsity level
#' @param maxIter maximum iteration
#' @return The solution of proximal gradient method with \eqn{l_{2,0}} regularizer.
#' @author Xinlin Hu <thompson-xinlin.hu@connect.polyu.hk>
#'
#' Yaohua Hu <mayhhu@szu.edu.cn>
#' @details The L2HardThr function aims to solve the problem:
#' \deqn{\min \|AX-B\|_F^2 + \lambda \|X\|_{2,0}}
#' to obtain s-joint sparse solution.
#' @export L2HardThr
#' @examples
#' m <- 256; n <- 1024; t <- 5; maxIter0 <- 50
#' A0 <- matrix(rnorm(m * n), nrow = m, ncol = n)
#' B0 <- matrix(rnorm(m * t), nrow = m, ncol = t)
#' X0 <- matrix(0, nrow = n, ncol = t)
#' NoA <- norm(A0, '2'); A0 <- A0/NoA; B0 <- B0/NoA
#' res_L20 <- L2HardThr(A0, B0, X0, s = 10, maxIter = maxIter0)
#'
L2HardThr <- function(A, B, X, s, maxIter = 200){
  # Initialization
  v <- 0.5 # stepsize
  Bu1 <- 2 * v * t(A) %*% B
  Bu2 <- 2 * v * t(A) %*% A

  for(k in 1:maxIter){
    # Gradient descent
    Bu <- X + Bu1 - Bu2 %*% X

    # L20 threhsolding operator
    normBu <- apply(Bu, 1, norm, '2') # L2 norm of each row
    Xnew <- Bu
    criterion <- sort(normBu, decreasing = T)[s+1]

    # Consider what if s-th largest group is not the only one
    if(criterion == sort(normBu, decreasing = T)[s]){
      ind <- which(normBu >= criterion)
    }else{
      ind <- which(normBu > criterion)
    }

    # Update matrix
    Xnew[-ind, ] <- 0

    if(norm(Xnew - X, 'f') <= 1e-6){ break }
    # Update and report
    X <- Xnew
    # message(paste('The', k, '-th iteration completes.'))
  }

  return(Xnew)
}